An Alternative Approach Towards the Higher Order Denoising of Images. Analytical Aspects

Abstract

Theoretical aspects of a variational model for the denoising of images which can be interpreted as a substitute for a higher order approach, are investigated. In this model, the smoothness term that usually involves the highest derivatives is replaced by a mixed expression for a second unknown function in which only derivatives of lower order occur. The main results concern the existence and uniqueness as well as the regularity properties of the solutions to this variational problem. They are established under various assumptions imposed on the growth rates of the different parts of the energy functional.